BTGModeratorVI wrote: ↑Fri Jul 03, 2020 6:55 am
A, B, C, and D are points on a line. If C is the midpoint of line segment AB and if D is the midpoint of line segment CB, is the length of line segment DB greater than 5?
1) The length of line segment AC is greater than 8
2) The length of line segment CD is greater than 6
Answer:
B
Source: Official guide
Given: A, B, C, and D are points on a line. If C is the midpoint of line segment AB and if D is the midpoint of line segment CB
When we sketch this information we get the following:
Notice that the two blue bars of equal length represent AC = CB, and the two red bars of equal length represent CD = DB.
Aside: The 4 points could also be arranged as B..D..C......A, but that doesn't change the answer to the question
Target question: Is the length of line segment DB greater than 5?
Statement 1: The length of line segment AC is greater than 8
There are several scenarios that satisfy statement 1. Here are two:
Case a: AC = 9.
In this case, the answer to the target question is
NO, line segment DB is NOT greater than 5
Case b: AC = 14.
In this case, the answer to the target question is
YES, line segment DB IS greater than 5
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The length of line segment CD is greater than 6
Since CD = DB, we can conclude that line segment DB IS greater than 6, which means
line segment DB IS greater than 5
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
